Aging statistics based on trapping/detrapping: Silicon evidence, modeling and long-term prediction

The aging process due to Negative Bias Temperature Instability (NBTI) exhibits a significant amount of variability and thus poses a dramatic challenge for long-term reliability prediction from short-term stress measurement. To develop a robust prediction method in this circumstance, this work first collects statistical device data from a 65nm test chip with a resolution of 0.2mV in threshold voltage (V_th) measurement. By comparing model prediction from short-term stress data (<;20k second) with direct long-term measurement (up to 200k second), we conclude that (1) the degradation follows a logarithmic dependence on time, as opposed to the conventional power law; (2) the Reaction-Diffusion (R-D) based tⁿ model significantly overestimates the aging rate and exaggerates its variance; (3) the log(t) model, derived from the trapping/de-trapping (T-D) mechanism, correctly captures the aging variability due to the randomness in number of available traps, and accurately predicts the mean and the variance of V_th shift. These results guide the development of a new aging model for robust long-term lifetime prediction.